## The Annals of Probability

### Large deviations for random walk in random environment with holding times

#### Abstract

Suppose that the integers are assigned the random variables $\{\omega_x,\mu_x\}$ (taking values in the unit interval times the space of probability measures on $\reals_+$), which serve as an environment. This environment defines a random walk $\{X_t\}$ (called a RWREH) which, when at x, waits a random time distributed according to $\mu_x$ and then, after one unit of time, moves one step to the right with probability $\omega_x$, and one step to the left with probability $1-\omega_x$. We prove large deviation principles for $X_t/t$, both quenched (i.e., conditional upon the environment), with deterministic rate function, and annealed (i.e., averaged over the environment). As an application, we show that for random walks on Galton--Watson trees, quenched and annealed rate functions along a ray differ.

#### Article information

Source
Ann. Probab., Volume 32, Number 1B (2004), 996-1029.

Dates
First available in Project Euclid: 11 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1079021470

Digital Object Identifier
doi:10.1214/aop/1079021470

Mathematical Reviews number (MathSciNet)
MR2044672

Zentralblatt MATH identifier
1126.60035

#### Citation

Dembo, Amir; Gantert, Nina; Zeitouni, Ofer. Large deviations for random walk in random environment with holding times. Ann. Probab. 32 (2004), no. 1B, 996--1029. doi:10.1214/aop/1079021470. https://projecteuclid.org/euclid.aop/1079021470

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